Compression therapy is used in the management and the treatment of various forms of venous insufficiency ranging from the relief of heavy and achy legs to the treatment of more severe forms such as acute venous ulceration. However, the pressure needed to achieve clinical benefit is a matter of debate. The purpose of this study was to examine the transmission of pressure within the soft tissues to improve current understanding of the mechanism of action of Medical Compression Stockings (MCS). Three-dimensional patient-specific finite element models were developed for six subjects. The geometry was obtained from CT-scans. Because experimental data on the mechanical properties of healthy adipose tissues and passive muscle are scarce in literature, an inverse method was setup to identify the constitutive properties of the said anatomical elements. This constitutes the original contribution of this work. The main outcome of this study is that the mean pressure applied by the MCS onto the skin is of the same order of magnitude as that applied by the compressed tissues onto the wall of the main deep veins, thereby suggesting that the mean pressure applied can be used as an indicator of the efficiency. Likewise, the maximal hydrostatic pressure in fat can be used to estimate the comfort.